Then have an official explicit EU-wide referendum.
The problem is that all 27 countries would have to unanimously agree to this as there is no constitutional basis for holding such a referendum at the moment. And in a purely EU wide referendum the smaller countries would be swamped, and therefor wouldn't agree to it. That is why we have a slow moving fudge - from unanimity to qualifies majority voting in more and more areas - the "qualified" majority being designed to ensure that larger countries can't railroad smaller ones, and that large majorities are required for changes. This is an improvement on unanimity, but even that small change has now been rejected and vetoed by 1% of the EU population. "It's a mystery to me - the game commences, For the usual fee - plus expenses, Confidential information - it's in my diary..."
You can't have (our usual kind of) democracy without the appearance of an explicit mandate. People really don't like it if you try to take that away from them, no matter how irrelevant it is in practice.
So given that Lisbon has been crafted to avoid the need for a formal popular mandate, it was never going to be acceptable.
The silliness about chipping babies and drafting them into the EU Child Zombie Flesh-Eating Radioactive Army would have been background noise if Lisbon had had a solid populist foundation.
(Not that I think that would help bringing such a referendum about. No doubt it would still be hard to achieve unanimous agreement amongst the 27 nations. But an EU-wide referendum does not have to mean straight up or down majority popular vote. However, such a plan would run into trouble with the German constitution, which I believe disallows referenda.)
